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Moments of generalized Motzkin paths.
2

%I #16 Oct 30 2022 18:19:59

%S 1,0,2,1,6,6,21,30,82,141,342,650,1485,2982,6612,13693,29922,63072,

%T 136905,291618,631302,1353441,2928054,6303798,13642117,29454702,

%U 63791456,138020533,299191968,648376932,1406836717,3052671816,6629649798,14400972413,31301837952

%N Moments of generalized Motzkin paths.

%H Michael De Vlieger, <a href="/A053442/b053442.txt">Table of n, a(n) for n = 2..2919</a>

%H R. A. Sulanke, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL3/SULANKE/sulanke.html">Moments of generalized Motzkin paths</a>, J. Integer Sequences, Vol. 3 (2000), #00.1.

%F G.f.: 1 / sqrt(1-4*z^2-2*z^3+z^6). - _Sean A. Irvine_, Dec 25 2021

%t CoefficientList[Series[1/Sqrt[1 - 4 x^2 - 2 x^3 + x^6], {x, 0, 34}], x], (* _Michael De Vlieger_, Dec 25 2021 *)

%K nonn,easy,nice

%O 2,3

%A _N. J. A. Sloane_, Jan 12 2000

%E More terms from _Reiner Martin_, Oct 13 2002

%E Typos in terms corrected by _Sean A. Irvine_, Dec 25 2021